From Proposition REF  it follows that \(L^2_V\) , \(L^2_H\)  and \(L^2_{V^*}\)  are Hilbert spaces with inner product defined by the formulae (REF ) and () and that \(L^2_V \subset L^2_H \subset L^2_{V^*}\)  is a Gelfand triple.
We note that \(\left(L^2_V\right)^*\)  is identified with \(L^2_{V^*}\) , for further properties of these spaces, we refer the reader to [1]}.
